Body surface area (Mosteller)

The formula

• BSA = √(h · m / 3600)

h is the height in centimetres, m the weight in kilograms and BSA the body surface area in square metres. The 3600 is the constant Mosteller fitted in 1987 so that one square root replaced the older formulas with their fractional exponents; the source is cited under the formula.

Holds when the body is of ordinary proportions. The constant was fitted to adults and children of usual build, and the result is an average for that height and weight, not a measurement of anyone’s skin.

A worked example

A man of 180 cm and 80 kg: BSA = √(180 · 80 / 3600) = √4 = 2.00 m². A woman of 165 cm and 60 kg: √(165 · 60 / 3600) = √2.75 = 1.66 m².

What it is for

Some drug doses, chemotherapy among them, are set per square metre of body surface rather than per kilogram, because the surface area tracks the metabolic rate better than the weight does. Cardiac output and kidney function are also reported per 1.73 m², a reference surface area. The number is a scaling figure for clinicians, not a health measure for the person.

The square root

Doubling the weight at the same height does not double the area: √2 ≈ 1.41, so the area rises by about 41%. That is the geometry of a body, which grows in three dimensions while its skin grows in two, and it is why the formula is a root rather than a product.

Common mistakes

• Height in metres or weight in pounds. The constant 3600 belongs to centimetres and kilograms; other units need other constants.
• Reading it as a target. Surface area says nothing about whether a weight is healthy; that question has the BMI and the waist-to-height ratio.
• Expecting agreement with other formulas. Du Bois, Haycock and Mosteller differ by a few per cent for the same person.

Frequently asked questions